1fcfll) 



.7 




, ^^ fFrotn the Journal of the Praaklin Institute, April, 1873.1 



TORSIONAL RESISTANCE OF MATERIALS DETERMINED BY A 
NEW APPARATUS WITH AUTOMATIC REGISTRY. . 

By Prof. R. H. Thurston. 

While the classes of the Stevens' Institute of Technology were re- 
cently engaged in their revision of coefficients, as given by various 
authorities on strength of materials, the difficulty of determining how 
far the differences noted were due to errors of observation, and how 
far to variation in the quality of the materials used, suggested to the 
writer the advisability of obtaining an apparatus which should make its 
own record. This could readily be done by so constructing it that a 
curve might be automatically registered at each tests, which should 
represent all circumstances of the experiment. 

Such an automatic registry would evidently yield more reliable 
and instructive information in regard to the circumstances of dis- 
tortion and fracture than could any system of personal observation. 

Representing the magnitude of the distorting stress at every in- 
stant, and under every degree of distortion of the material, up to the 
limit of elasticity or even to the point of rupture, and exhibiting also 
the corresponding alteration of form at every point, the pencilled 
curve would be a record from which might be deduced the coefficients 
of elasticity, strength and resilience, as well as the laws governing 
the relations of the distorting forces to the resistance of the material. 

A simple but effective machine was therefore designed and con- 
structed, which accomplishes satisfactorily the desired result, and 
this machine, as planned by the writer and constructed by Messrs. 
Hawkins & Wales, instrument makers to the Institute, is shown in 
Fig. 1. 

As here arranged, it is intended for experiments on the torsion of 
materials. Its modifications, for the purpose of experimenting upon 
transverse strength, will be described in a subsequent paper, in which 
will be given the results of that series of experiments. 

In the figure, the frame, A A, A'A r , supports two suspended arms, 
C E, B D, which swing about independent axes in the same line. The 
arm, B, carries at its extremity a weight, D, and the arm, C, has a han- 
dle, E, by which it is moved. The axes of these arms are designed 
as shown in Fig. 2, each having a rectangular recess at L and at M, 
which receive each an end of the test piece, which is squared to fit, 
as shown in Figs. 3 and 4. 



The frame, A'A', carries a guide curve, F, of s 



ordinates are proportional to the 




uch form that its 
twining moments exerted by the 



FiG.2 




Fig. 3 




Fig. 4 




weighted arm B D, while swinging through the arc to which the cor. 
responding abscisses are proportional. >A pencil holder, I bears 
against this guide curve, and, being carried by the weighted 'arm is 
thrown forward, as that arm swings out under the action of the fo ce 
producing torsion, which force is transmitted through the test piece. 
The arm, C E, carries a table, G, and the pencil, I, therefore, traces 
upon the paper, which is clamped upon it, a curve, the ordinates of 
winch are proportional to the torsional moments, while its abscisses 
represent the relative motion of the two arms, and, consequent tli 
amount of torsion to winch the test piece has been subjected. 

The curves thus described, of which the accompanying plate exhib- 

its a number, present, in a very legible and convenient we 1 as 

"'.able, form, all the results of the experiment,, of which they are 

the respective records. •> e 

M» PO»*jr, J, traversing the are, K K, is arranged as a maximum 
hau^andaiWdsau.e.uUhcc.u, the automatic record of max, 



•\h 



The plate represents the results of average experiments made upon 
a considerable number of varieties of wood, the test pieces of the 
form shown in Fig. 8 being used. The diameter of the neck of each 
piece was seven-eighths (J) of an inch. 

This diameter happened to be that best adapted to use in this ma- 
chine. A larger size was found, frequently, to yield by the destruc- 
tion of lateral cohesion, the square head peeling, leaving a prolonga- 
tion of the cylindrical portion, instead of twisting off in the neck. 
This size is convenient, also, in consequence of the fact that the co- 
efficient of ultimate strength for the standard diameter of one inch is 
obtained, with a close approximation to exactness, by simply multi- 
plying the twisting moment for each piece by 1*5. 

These curves exhibit the relative stiffness, strength and resilience 
of the woods tested very perfectly. The inclination of the straight 
line, forming the first portion of each diagram, from the vertical is a 
measue of stiffness ; the height of the maximum ordinate indicates 
the ultimate strength ; the point at which deviation from this straight 
line commences, determines the limit of elasticity, and the area in- 
cluded within each diagram is proportional to the torsional resilience 
of the test piece. 

The fact that the commencement is, in each case, almost a perfectly 
straight line, is well exhibited in the curve, a a a, of locust, where 
the horizontal scale is purposely magnified, justifies the usual assump- 
tion that, up to the limit of elasticity, Hooke's law is correct, and 
that the angle of torsion is proportional to the twisting moment. 

The short curve of small radius, noticed at the foot of the straight 
portion of each line, is produced by the slight yielding of the test 
piece by crushing, where it is grasped by the machine, which yield- 
ing continues until a firm hold has been secured. 

It will be observed that, in most cases, the torsional resistance in- 
creases with the total angle of torsion up to a maximum, then, pass- 
ing the limit of elasticity, it drops off more or less rapidly, returning 
finally to zero. In the brittle woods, the fall takes place suddenly, 
while, in the tougher and more elastic varieties, the resistance de- 
creases very slowly, in some cases vanishing only after the test piece 
has been twisted through a very large angle. 

In the case of black walnut^ 6, 6,Q; locust, 11, 11, 11, and, in a 
still more remarkable manner, in that of hickory, 10, 10, 10, a strik- 
ing peculiarity is exhibited, which is one of the most interesting and 
unanticipated developments of this series of experiments. In these 



/ 



curves the resistance increases with the amount of torsion, until a 
maximum is reached ; the line then drops to a point considerably 
below, and thence again rises and passes another maximum, which, 
in the case of hickory, is only reached after a torsion of 75°. The 
resisting moment there becomes considerably greater than at the limit 
of elasticity. 

This striking peculiarity was shown, by carefully repeated experi- 
ment, to be due to the fact that, in those woods in which it was no- 
ticed, the lateral cohesion seemed much less, in proportion to the 
longitudinal strength, than in other varieties. "Watching the process 
of yielding under stress, it could be seen, by close observation, that, 
in the examples now referred to, the first maximum was passed at 
the instant when, the lateral cohesion of the fibres being overcome, 
they slipped upon each other, and the bundle of, then, loose fibres 
readily yielding, the curve dropped until, by lateral crowding, further 
movement was checked and the resistance again rose until the second 
maximum was reached. Here yielding again commenced, this time 
by the breaking of the fibres under longitudinal stress, — under that 
component of torsional stress which takes a direction parallel with 
that of the fibres, in their new positions. In these cases rupture 
seems never to occur by true shearing in the transverse plane. The 
fibres part, one after another, the exterior ones breaking first, under 
a tensile stress. 

The following varieties of ,wood have been subjected to torsional 
fracture, and the curves obtained are shown in the plate which illus- 
trates this article : 

1. White Pine, (Pinus strobus.) 

2. S. Yellow Pine (Pinus australis), sap wood. 

3. " " " " heart wood. 

4. Black Spruce (Abies nigra). 

5. Ash (Fraxinus Americana). 

6. Black Walnut (Juglans nigra). 

7. Red Cedar (Juniper is Virginianus). 

6. Spanish Mahogany (Swietenia maltogani). 

9. White Oak (Quercus alba). 

10. Hickory {Juglans alba). 

11. Locust (Robinia pseudo-acacia). 

12. Chestnut (Castanea esca). 

The curves, the fac similes of which are given in the plate, exhibit 



k 



5 

well the relative values of the materials tested for the various pur- 
poses to which they may be applied. 

White pine, 1, 1, 1, yields quite rapidly as the torsional moment 
increases, and the considerable inclination of the line from the verti- 
cal indicates its deficiency in stiifness. It soon reaches the limit of 
elasticity, and the diagram exhibits the maximum strength of the 
test piece, 15J foot-pounds. Passing the limit of elasticity and the 
maximum moment of resistance almost simultaneously, its resisting 
power decreases rapidly, and with tolerable uniformity, until, at " a 
total angle of torsion'' of 130°, it is twisted completely off. The 
area comprised within the curve is comparatively small and it is thus 
shown to have little resilience. 

Yellow pine, in accordance with our already well established ideas 
of its properties, is found by an examination of its curve, 2, 2, 2, 
3, 3, 3, to have much greater stiffness, strength and resilience. The 
sap wood, 2, 2, 2, is equally stiff, in the examples tested, with the 
heart wood, 3, 3, 3, 3, but sooner passes its limit of elasticity, the 
former circumstance being quite opposed to the preconceived ideas of 
the writer. Notwithstanding the comparatively low position occupied 
by the pines in our list, they are excellent materials, the yellow va- 
rieties particularly, for general purposes. Our comparison is made 
with specimens of equal size, and the important fact of the excep- 
tional lightness of these woods is nowhere brought to our notice by 
these tests. 

Spruce, 4, 4, 4, 4, is less stiff than white pine, even, but possesses 
greater strength and resilience, its moment of resistance reaching 18 
foot-pounds, and twisting through a total angle of torsion of 200°. 

Ash, 5, 5, 5, 5, seems to be weaker and less tough than is gener- 
ally supposed - ; it is possible that the specimens tested were over 
seasoned. Its most striking peculiarity is its very rapid loss of 
strength after passing its limit of elasticity. 

Black walnut, 6, 6, 6, (3, of the excellent quality and good condi- 
tion, as regards seasoning, of the samples tried, is very stiff, strong 
and resilient, and is but little inferior to oak. Its resisting moment 
reaches 35 foot-pounds, and one specimen reaches a total angle of 
torsion of 220°. 

Red cedar, 7, 7, 7, 7, is stiff, but brittle, and loses all power of re- 
sistance after twisting through an angle of 92°. A torsional moment 
of 20 foot-pounds only produces a total angle of torsion of 5°. 

Spanish mahogany, 8, 8, 8, 8, is very stiff and strong. It is de- 



ficient in toughness and resilience, losing its power of resistance very 
rapidly after passing the limit of elasticity. 

White oak, 9, 9, 9, 9, has less torsional strength than either good 
mahogany, locust or hickory, but is remarkable for its wonderful 
toughness. It passes its limit of elasticity at 15°, but loses its re- 
sisting power'Very slowly indeed. We find the latter almost unim- 
paired until it has been subjected to a torsion of 70° ; it only yielded 
completely at 253°. 

Millwrights are evidently perfectly correct in holding this wood in 
high esteem for strength, toughness and power of resisting heavy 
shocks and strains. 

Hickory, 10, 10, 10, 10, exhibits, in its curve, the remarkable pair 
of maxima already referred to, and has, apparently, the highest ulti- 
mate torsional strength, combined with unusual stiffness and consid- 
erable resilience. Its moment of resistance to torsion reaches a 
maximum of 58 foot-pounds. 

Locust, 11, 11, 11, 11, has greater stiffness than any other wood 
in our list, and stands next to hickory in strength ; it is, also, very 
resilient. Three diagrams are given, each of which possesses its own 
peculiarities. One specimen is only twisted through a total angle of 
torsion of 4° by a torsional moment of 48 faot-pounds. 

Where more than one curve is given for. the same wood, it is a fact 
worth noticing that the stiffness and ultimate strength are usually 
very nearly equal, and that the difference between the several speci- 
mens becomes marked, if at all, in their degrees of toughness. 

In the formula for torsional strength, Pa = Cd 3 , the curves give, 
values of C, as follows : 



1. White Pine, . . 25 7. Red Cedar, 

2. Yellow " sap, . 35 8. Spanish Mahogany, 

3. " " heart, . 40 9. Oak, 

4. Spruce . . .30 10. Hickory, . 

5. Ash, .... 43 11. Locust, 

6. Black Walnut, . . 55 12. Chestnut, 



32 
65 
53 
85 
80 
35 

Determining relative stiffness by obtaining values of the ratio of 
twisting moment to the total angle of torsion we obtain the following: 

4-00 

2-53 
4-15 
5-50 

1C0 



1. White Pine, . . 1-00 7. Red Cedar, 

2. Yellow " sap, . 2-25 8. Spanish Mahogany, 

3. " " heart, . 2^25 9. Oak, 

4. Spruce, . . . 0*67 10. Hickory. . 

5. Ash, . . . 1.87 11. Locust, 
G Black Walnut, . . 2'68 12. Chestnut, . 



Taking the well established value for oak as a standard, we deduce 
the following values for the coefficient to be used in the formula, 
2 Pa Total Angle of Torsion. 





G^r 4 Length of Part Twisted. 




1. 


White Pine, . . 220,000 7. Red Cedar/. ( . 


890,000 


2. 


Yellow " sap, . 495,000 8. Spanish Mahogany, 


, 660,000 


3. 


" heart,. 495,000 9. Oak, . 


570,000 


4. 


Spruce, . . 211,000 10. Hickory, . 


910,000 


5. 


Ash, . . . 410,000 11. Locust, 


1,225,000 


6. 


Black Walnut, . 582,000 12. Chestnut, . 


355,000. 



Finally, by measuring the areas of the several curves, we deduce 
the following values for relative resilience, white pine being taken as 
the standard : 

The work done in twisting oiF these specimens is found to have 
relative values as follows : 

7. Red Cedar, . . . 1-61 

8. Spanish Mahogany, 2*25; 1*65 

9. Oak, .... 6-60 

10. Hickory, . . . 6-&0 

11. Locust, . 7-65; 5-85; 320 

12. Chestnut, . . . 2-40 
The values of coefficients, as given, will be checked by additional 

experiments upon test pieces of the form shown in figure 4, carefully 
turned to a diameter of f inch, and of a length, in the neck, of one 
inch. 

Coefficients for metals will also be given in a later communication. 

Stevens Institute of Technology, HoboJcen, iV. J. y Feb., 1873. 



1. 


White Pine, . 


1-00 


2. 


Yellow " sap, . 


3-01 


3. 


" " heart, 


3-87 


4. 


Spruce, 


1-50 


5. 


Ash,^ . 


2-25 


6. 


Black Walnut, 5-00 ; 


3-95 



LIBRARY OF CONGRESS 



019 410 152 1 



, 



LIBRARY OF CONGRESS 



019 410 152 1 



Hollinger Corp. 
pH 8.5 



